This is not very intuitive:
sage: sqrt(3) in QQ[sqrt(3)]
False
sage: QQ[sqrt(3)]
Number Field in sqrt3 with defining polynomial x^2 - 3
On Sun, Oct 07, 2012 at 08:23:20AM -0700, Greg Laun wrote:
> __contains__ is broken in general and special linear groups. For example:
>
> sage: identity_matrix(GF(2),2) in GL(2,CC)
> True
>
> The base field of the matrix is characteristic 2, but it's reported as being a matrix over C.
>
> I reported this to sage-devel here:
https://groups.google.com/forum/?fromgroups=#!searchin/sage-devel/laun/sage-devel/WwovHNaUldE/lt2pFK6BeJsJ
> It contains some discussion, including why using the boilerplate __contains__ probably won't work.
>
> I was about to submit a bug report, when I noticed the wiki telling me to email sage-support first. I already emailed sage-devel, so I hope I'm not spamming too much by also emailing here.
>
>